An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists
An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists
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DOI：
10.1007/978-3-642-30805-5
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发表时间：
2012-07
期刊：
影响因子：
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通讯作者：
H. Ishimori;Tatsuo C. Kobayashi;H. Ohki;H. Okada;Yusuke Shimizu;M. Tanimoto
中科院分区：
文献类型：
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作者：
H. Ishimori;Tatsuo C. Kobayashi;H. Ohki;H. Okada;Yusuke Shimizu;M. Tanimoto
这些课堂讲稿提供了一个非阿贝尔离散群的复习教程，并展示了一些在物理问题上的应用，其中离散对称性构成了粒子物理模型构建的重要原则。虽然阿贝尔离散对称通常是为了控制粒子物理的耦合而强加的，特别是在标准模型之外的模型构建中，但非阿贝尔离散对称已被应用于理解三代风味结构。事实上，非阿贝尔离散对称被认为是风味领域最具吸引力的选择：模型构建者试图通过假设夸克和轻子的非阿贝尔离散风味对称来推导夸克和轻子质量和混合角的实验值，然而，轻子混合也已经在这方面得到了深入的讨论。味道的非阿贝尔离散对称的可能起源是另一个有趣的话题，因为它们可以从一个潜在的理论中产生-例如弦理论或通过轨道折叠的紧化-从而在潜在理论和相应的低能量粒子物理领域之间提供了一个可能的桥梁。本文明确地介绍和研究了许多具体群体的群论方面，并展示了如何推导共轭类，字符，表示和张量积为这些群体（与有限的数字）当代数关系给出，从而使读者能够将此应用到其他群体的兴趣。
These lecture notes provide a tutorial review of non-Abelian discrete groups and show some applications to issues in physics where discrete symmetries constitute an important principle for model building in particle physics. While Abelian discrete symmetries are often imposed in order to control couplings for particle physics-in particular model building beyond the standard model-non-Abelian discrete symmetries have been applied to understand the three-generation flavor structure in particular. Indeed, non-Abelian discrete symmetries are considered to be the most attractive choice for the flavor sector: model builders have tried to derive experimental values of quark and lepton masses, and mixing angles by assuming non-Abelian discrete flavor symmetries of quarks and leptons, yet, lepton mixing has already been intensively discussed in this context, as well. The possible origins of the non-Abelian discrete symmetry for flavors is another topic of interest, as they can arise from an underlying theory-eg the string theory or compactification via orbifolding–thereby providing a possible bridge between the underlying theory and the corresponding low-energy sector of particle physics. This text explicitly introduces and studies the group-theoretical aspects of many concrete groups and shows how to derive conjugacy classes, characters, representations, and tensor products for these groups (with a finite number) when algebraic relations are given, thereby enabling readers to apply this to other groups of interest.